Deck 17: Graphs of the Trigonometric Functions

Question 1

Determine the period, frequency, and amplitude for this periodic waveform:

Answer 1

period $=3$ , frequency $=1 / 3$ , amplitude $=3$

Question 2

Determine the period, frequency, and amplitude for this periodic waveform:

Answer 2

period $=2$ , frequency $=1 / 2$ , amplitude $=2$

Question 3

Determine the period, frequency, and amplitude for this periodic waveform:

Answer 3

period $=2$ , frequency $=1 / 2$ , amplitude $=1$

Question 4

Graph $y=4 \sin x$ . Determine the amplitude and period.

Question 5

Graph $y=12 \sin x$ . Determine the amplitude and period.

Question 6

Graph $y=-\sin x$ . Determine the amplitude and period.

Question 7

Graph $y=5 \sin 2 x$ . Determine the amplitude, period, and phase shift.

Question 8

Graph $y=3.5 \sin \pi x$ . Determine the amplitude, period, and phase shift.

Question 9

Graph $y=-12 \sin 4 x$ . Determine the amplitude, period, and phase shift.

Question 10

Graph $y=-3 \sin (3 x-6 \pi)$ . Determine the amplitude, period, and phase shift.

Question 11

Graph $y=5 \sin \left(2 x-45^{\circ}\right)$ . Determine the amplitude, period, frequency, and phase shift.

Question 12

Graph $y=0.2 \sin 3 \pi x$ . Determine the amplitude, period, frequency, and phase shift.

Question 13

Graph $y=\sin \left(x-\frac{3 \pi}{2}\right)$ . Determine the amplitude, period, frequency, and phase shift.

Question 14

Graph $y=\cos \left(x-\frac{3 \pi}{8}\right)$ . Determine the amplitude, period, frequency, and phase shift.

Question 15

Write the equation of a sine function that has an amplitude of 100 , a period of 8 , and a phase shift of 4 to the right.

Question 16

Write the equation of a sine function that has an amplitude of 3 , a period of 2 , and a phase shift of 1 to the left.

Question 17

Write the equation of a sine curve that has an amplitude of 3 , a period of $3 \pi$ , and a phase shift of $\pi / 3$ .

Question 18

Write the equation of a sine curve that has an amplitude of $\pi$ , a period of $\pi$ , and a phase shift of 0 .

Question 19

Write the equation of a sine curve that has an amplitude of 10 , a period of $5 \pi$ , and a phase shift of $\pi / 2$ .

Question 20

Write the equation of a sine curve that has an amplitude of 6 , a period of $3 \pi$ , and a phase shift of $-2 \pi$ .

Question 21

Graph $y=3 \cos (2 x-\pi)$ . Determine the amplitude, period, and phase shift.

Question 22

Graph $y=\cos (\pi x+\pi)$ . Determine the amplitude, period, and phase shift.

Question 23

Graph the function $y=3 \tan 5 x$ .

Question 24

Graph the function $y=2 \tan 3 x$ .

Question 25

Graph the function $y=0.25 \sec (2 x)$

Question 26

Graph the function $y=\sec (2 x+5)$ .

Question 27

Graph the function $y=1.5 \csc 1.5 x$ .

Question 28

Graph the function $y=2 \cot (3 x+1)$ .

Question 29

Graph the function $y=x^{2}+\sin x$ .

Question 30

Graph the function $y=4 \csc (3 x+4)$ .

Question 31

Graph the function $y=3 x-5 \cos (2 x)$ .

Question 32

Graph the function $y=5 x^{2}+2 \sin (2 \pi x-5)$ .

Question 33

Graph the function $y=\sqrt{x}+\cos 2 x$ .

Question 34

Graph the function $y=\sin 2 x+\cos x$ .

Question 35

Graph the function $y=\sin x+\cos 3 x$ .

Question 36

Find the period and angular velocity of a repeating waveform that has a frequency of $28 \mathrm{~Hz}$ .

Question 37

Find the period and angular velocity of a repeating waveform that has a frequency of $72 \mathrm{~Hz}$ .

Question 38

Find the period and angular velocity of a repeating waveform that has a frequency of $66.5 \mathrm{~Hz}$ .

Question 39

Find the frequency (in $\mathrm{Hz}$ ) and angular velocity of a repeating waveform whose period is $2 \mathrm{~s}$ .

Question 40

Find the frequency (in $\mathrm{Hz}$ ) and angular velocity of a repeating waveform whose period is $14 \mathrm{~s}$ .

Question 41

Express $y=74.1 \sin w t+85.2 \cos w t$ as a single sine wave.

Question 42

Express $y=21.5 \sin w t+22.5 \sin \left(w t+30.0^{\circ}\right)$ as a single sine wave.

Question 43

Express $y=13 \sin w t+17$ coswt as a single sine wave.

Question 44

Write an equation for an alternating voltage that has a peak value of $125 \mathrm{~V}$ , a frequency of $55 \mathrm{~Hz}$ , and a phase angle of $18.0^{\circ}$ .

Question 45

Write an equation for an alternating current that has a peak amplitude of $42.4 \mathrm{~mA}$ , a frequency of 35 $\mathrm{Hz}$ , and a phase angle of $42.1^{\circ}$ .

Question 46

Plot the point $\left(3.5,15^{\circ}\right)$ , given in polar coordinates.

Question 47

Plot the point $\left(6,-205^{\circ}\right)$ , given in polar coordinates.

Question 48

Express $(-2,3)$ in polar coordinates to three significant digits.

Question 49

Express $(5.96,-8.23)$ in polar coordinates.

Question 50

Write the rectangular coordinates of $\left(3.14,124^{\circ}\right)$ .

Question 51

Write the rectangular coordinates of $(2,-\pi / 4)$ to three significant digits.

Question 52

Write polar coordinates of each point:
(a) $(3.00,4.00)$
(b) $(2.00,5.00)$
(c) $(-5.00,-1.00)$
(d) $(-1.00,5.00)$

Question 53

Write rectangular coordinates of each point:
(a) $\left(6.00,23.0^{\circ}\right)$
(b) $\left(2.00,197^{\circ}\right)$
(c) $(5.00,-3 \pi / 4)$
(d) $(19.1,-\pi / 7)$

Question 54

Express $(2.50,-3.20)$ in polar coordinates.

Question 55

Express $(-7.00,-3.25)$ in polar coordinates.

Question 56

Graph the equation $r=2+2 \cos \theta$ , given in polar coordinates.

Question 57

Graph the equation $r=\sin \theta+1$ , given in polar coordinates.

Question 58

Transform the polar equation $r=3 \cos \theta$ into rectangular form.

Question 59

Transform the polar equation $r=3 \sin \theta$ into rectangular form.

Question 60

Transform the rectangular equation $x^{2}+y^{2}=16$ into polar form.

Question 61

Transform the rectangular equation $x+3 y=4$ into polar form.

Question 62

Write the polar equation $r=4 \sin \theta+3 \cos \theta$ in rectangular form.

Question 63

Write the rectangular equation $y=-5 x^{2}$ in polar form.

Question 64

Write the polar equation $r=25$ in rectangular form.

Question 65

Graph the parametric equations: $x=\sin \theta, y=-2 \sin \theta$

Question 66

Graph the parametric equations: $x=3 \sin \theta, y=\sin \theta$

Question 67

Graph the parametric equations: $x=2 \cos \theta, y=6 \cos \theta$

Question 68

Rewrite $r=3$ in parametric form, and graph.

Question 69

Rewrite $r=2 \cos \theta$ in parametric form, and graph.

Question 70

Rewrite $r=2 \sin \theta$ in parametric form, and graph.